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Harmonic analysis on totally disconnected groups and irregularities of point distributions
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M. M Skriganov
Published/Copyright:
November 20, 2006
Abstract
The goal of this paper is to study point distributions in the multi-dimensional unit cube which possess the structure of finite abelian groups with respect to certain p-ary arithmetic operations. Such distributions can be thought of as finite subgroups in a compact totally disconnected group of the Cantor type. We apply the methods of Lq harmonic analysis to estimate very precisely the Lq-discrepancies for such distributions. Following this approach, we explicitly construct point distributions with the minimal order of the Lq-discrepancy for each q, 1 < q < ∞.
Received: 2003-07-10
Revised: 2005-10-13
Published Online: 2006-11-20
Published in Print: 2006-11-01
© Walter de Gruyter
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Articles in the same Issue
- Exterior products of zero-cycles
- Harmonic analysis on totally disconnected groups and irregularities of point distributions
- Relative cyclic homology of square zero extensions
- Weighted Fano threefold hypersurfaces
- Surfaces expanding by the inverse Gauß curvature flow
- Symplectic singularities from the Poisson point of view
- Multiplicative rule in the Grothendieck cohomology of a flag variety
- Generalized double affine Hecke algebras of higher rank
- Defining relations of the tame automorphism group of polynomial algebras in three variables
